#include <stdio.h>
#include <conio.h>
#include <math.h>

#define MAX 3

void matrix ( int [3][3] ) ;
void create ( int [3][3] ) ;
void display ( int [3][3] ) ;
void matmul ( int [3][3], int [3][3], int [3][3] ) ;
void transpose ( int [3][3], int [3][3] ) ;
int determinant ( int [3][3] ) ;
int isortho ( int [3][3] ) ;

void main( )
{
int mat [3][3], d ;

clrscr( ) ;

printf ("\nEnter elements for array: \n\n") ;
create ( mat ) ;

printf ("\nThe Matrix: \n") ;
display ( mat ) ;

d = determinant ( mat ) ;
printf ("\nThe determinant for given matrix: %d.\n",d) ;

if ( d == 0 )
printf ("\nMatrix is singular.\n") ;
else
printf ("\nMatrix is not singular.\n") ;

d = isortho ( mat ) ;

if ( d != 0 )
printf ("\nMatrix is orthogonal.\n") ;
else
printf ("\nMatrix is not orthogonal.\n") ;

getch( ) ;
}

void matrix ( int mat[3][3] )
{
int i, j ;
for ( i = 0 ; i < MAX ; i++ )
{
for ( j = 0 ; j < MAX ; j++ )
mat[i][j] = 0 ;
}
}

void create ( int mat[3][3] )
{
int n, i, j ;
for ( i = 0 ; i < MAX ; i++ )
{
for ( j = 0 ; j < MAX ; j++ )
{
printf ("Enter the element: ") ;
scanf ("%d",&n) ;
mat[i][j] = n ;
}
}
}

void display ( int mat[3][3] )
{
int i, j ;
for ( i = 0 ; i < MAX ; i++ )
{
for ( j = 0 ; j < MAX ; j++ )
printf ("%d\t", mat[i][j] ) ;
printf ("\n") ;
}
}
void matmul ( int mat1[3][3], int mat2[3][3], int mat3[3][3] )
{
int i, j, k ;
for ( k = 0 ; k < MAX ; k++ )
{
for ( i = 0 ; i < MAX ; i++ )
{
mat3[k][i] = 0 ;
for ( j = 0 ; j < MAX ; j++ )
mat3[k][i] += mat1[k][j] * mat2[j][i] ;
}
}
}

void transpose ( int mat[3][3], int m[3][3] )
{
int i, j ;
for ( i = 0 ; i < MAX ; i++ )
{
for ( j = 0 ; j < MAX ; j++ )
m[i][j] = mat[j][i] ;
}
}

int determinant( int mat[3][3] )
{
int sum, i, j, k, p ;
sum = 0 ; j = 1 ; k = MAX - 1 ;

for ( i = 0 ; i < MAX ; i++ )
{
p = pow ( -1, i ) ;

if ( i == MAX - 1 )
k = 1 ;
sum = sum + ( mat[0][i] * ( mat[1][j] * mat[2][k] - mat[2][j] * mat[1][k] ) ) * p ;
j = 0 ;
}

return sum ;
}

int isortho ( int mat[3][3] )
{

int m1[3][3], m2[3][3], i ;
transpose ( mat, m1 ) ;

matmul ( mat, m1, m2 ) ;

for ( i = 0 ; i < MAX ; i++ )
{
if ( m2[i][i] == 1 )
continue ;
else
break ;
}
if ( i == MAX )
return 1 ;
else
return 0 ;
}